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| <div class="title">dense_linear_systems.sql_in</div> </div> |
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| <div class="contents"> |
| <div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">/* ----------------------------------------------------------------------- */</span><span class="comment">/**</span></div> |
| <div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment"> * @file dense_linear_sytems.sql_in</span></div> |
| <div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment"> * @brief SQL functions for linear systems</span></div> |
| <div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment"> * @date January 2011</span></div> |
| <div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment"> * @sa Computes the solution of a consistent linear system</span></div> |
| <div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment"> */</span><span class="comment">/* ----------------------------------------------------------------------- */</span></div> |
| <div class="line"><a name="l00011"></a><span class="lineno"> 11</span> </div> |
| <div class="line"><a name="l00012"></a><span class="lineno"> 12</span> m4_include(`SQLCommon.m4<span class="stringliteral">')</span></div> |
| <div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment">@addtogroup grp_dense_linear_solver</span></div> |
| <div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="comment"><div class ="toc"><b>Contents</b></span></div> |
| <div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="comment"><ul></span></div> |
| <div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="comment"><li class="level1"><a href="#dls_about">About</a></li></span></div> |
| <div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="comment"><li class="level1"><a href="#dls_online_help">Online Help</a></li></span></div> |
| <div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="comment"><li class="level1"><a href="#dls_function">Function Syntax</a></li></span></div> |
| <div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="comment"><li class="level1"><a href="#dls_args">Arguments</a></li></span></div> |
| <div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="comment"><li class="level1"><a href="#dls_opt_params">Optimizer Parameters</a></li></span></div> |
| <div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="comment"><li class="level1"><a href="#dls_output">Output Tables</a></li></span></div> |
| <div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="comment"><li class="level1"><a href="#dls_examples">Examples</a></li></span></div> |
| <div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="comment"></ul></span></div> |
| <div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="comment"></div></span></div> |
| <div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="comment">@anchor dls_about</span></div> |
| <div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="comment">@about</span></div> |
| <div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="comment">The linear systems module implements solution methods for systems of consistent</span></div> |
| <div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment">linear equations. Systems of linear equations take the form: </span></div> |
| <div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="comment">\f[</span></div> |
| <div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment"> Ax = b</span></div> |
| <div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="comment">\f]</span></div> |
| <div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="comment">where \f$x \in \mathbb{R}^{n}\f$, \f$A \in \mathbb{R}^{m \times n} \f$ and \f$b \in \mathbb{R}^{m}\f$. </span></div> |
| <div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment">We assume that there are no rows of \f$A\f$ where all elements are zero. </span></div> |
| <div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="comment">The algorithms implemented in this module can handle large dense</span></div> |
| <div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="comment">linear systems. Currently, the algorithms implemented in this module</span></div> |
| <div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="comment">solve the linear system by a direct decomposition. Hence, these methods are </span></div> |
| <div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="comment">known as <em>direct method</em>. </span></div> |
| <div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="comment">@anchor dls_online_help</span></div> |
| <div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="comment">@par Online Help</span></div> |
| <div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="comment">View short help messages using the following statements:</span></div> |
| <div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="comment">@verbatim </span></div> |
| <div class="line"><a name="l00052"></a><span class="lineno"> 52</span> <span class="comment">-- Summary of dense linear systems</span></div> |
| <div class="line"><a name="l00053"></a><span class="lineno"> 53</span> <span class="comment">SELECT madlib.linear_solver_dense();</span></div> |
| <div class="line"><a name="l00054"></a><span class="lineno"> 54</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00055"></a><span class="lineno"> 55</span> <span class="comment">-- Function syntax and output table format</span></div> |
| <div class="line"><a name="l00056"></a><span class="lineno"> 56</span> <span class="comment">SELECT madlib.linear_solver_dense('usage');</span></div> |
| <div class="line"><a name="l00057"></a><span class="lineno"> 57</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00058"></a><span class="lineno"> 58</span> <span class="comment">-- Syntax for direct methods</span></div> |
| <div class="line"><a name="l00059"></a><span class="lineno"> 59</span> <span class="comment">SELECT madlib.linear_solver_dense('direct');</span></div> |
| <div class="line"><a name="l00060"></a><span class="lineno"> 60</span> <span class="comment">@endverbatim</span></div> |
| <div class="line"><a name="l00061"></a><span class="lineno"> 61</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00062"></a><span class="lineno"> 62</span> <span class="comment">@anchor dls_function</span></div> |
| <div class="line"><a name="l00063"></a><span class="lineno"> 63</span> <span class="comment">@par Function Syntax</span></div> |
| <div class="line"><a name="l00064"></a><span class="lineno"> 64</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00065"></a><span class="lineno"> 65</span> <span class="comment"><pre></span></div> |
| <div class="line"><a name="l00066"></a><span class="lineno"> 66</span> <span class="comment">SELECT linear_solver_dense(tbl_source, tbl_result, row_id, LHS, </span></div> |
| <div class="line"><a name="l00067"></a><span class="lineno"> 67</span> <span class="comment"> RHS, grouping_col := NULL, optimizer := 'direct', </span></div> |
| <div class="line"><a name="l00068"></a><span class="lineno"> 68</span> <span class="comment"> optimizer_params := 'algorithm = householderqr');</span></div> |
| <div class="line"><a name="l00069"></a><span class="lineno"> 69</span> <span class="comment"></pre></span></div> |
| <div class="line"><a name="l00070"></a><span class="lineno"> 70</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00071"></a><span class="lineno"> 71</span> <span class="comment">@anchor dls_args</span></div> |
| <div class="line"><a name="l00072"></a><span class="lineno"> 72</span> <span class="comment">@par Arguments</span></div> |
| <div class="line"><a name="l00073"></a><span class="lineno"> 73</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00074"></a><span class="lineno"> 74</span> <span class="comment"><DL class="arglist"></span></div> |
| <div class="line"><a name="l00075"></a><span class="lineno"> 75</span> <span class="comment"><DT>tbl_source</DT></span></div> |
| <div class="line"><a name="l00076"></a><span class="lineno"> 76</span> <span class="comment"><DD>Text value. The name of the table containing the training data.</span></div> |
| <div class="line"><a name="l00077"></a><span class="lineno"> 77</span> <span class="comment">The input data is expected to be of the following form:</span></div> |
| <div class="line"><a name="l00078"></a><span class="lineno"> 78</span> <span class="comment"><pre>{TABLE|VIEW} <em>sourceName</em> (</span></div> |
| <div class="line"><a name="l00079"></a><span class="lineno"> 79</span> <span class="comment"> ...</span></div> |
| <div class="line"><a name="l00080"></a><span class="lineno"> 80</span> <span class="comment"> <em>row_id</em> FLOAT8,</span></div> |
| <div class="line"><a name="l00081"></a><span class="lineno"> 81</span> <span class="comment"> <em>left_hand_side</em> FLOAT8[],</span></div> |
| <div class="line"><a name="l00082"></a><span class="lineno"> 82</span> <span class="comment"> <em>right_hand_side</em> FLOAT8,</span></div> |
| <div class="line"><a name="l00083"></a><span class="lineno"> 83</span> <span class="comment"> ...</span></div> |
| <div class="line"><a name="l00084"></a><span class="lineno"> 84</span> <span class="comment">)</pre></span></div> |
| <div class="line"><a name="l00085"></a><span class="lineno"> 85</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00086"></a><span class="lineno"> 86</span> <span class="comment">Here, each row represents a single equation using. The <em> right_hand_side </span></div> |
| <div class="line"><a name="l00087"></a><span class="lineno"> 87</span> <span class="comment"></em> refers</span></div> |
| <div class="line"><a name="l00088"></a><span class="lineno"> 88</span> <span class="comment">to the right hand side of the equations while the <em> left_hand_side </em></span></div> |
| <div class="line"><a name="l00089"></a><span class="lineno"> 89</span> <span class="comment">refers to the multipliers on the variables on the left hand side of the same</span></div> |
| <div class="line"><a name="l00090"></a><span class="lineno"> 90</span> <span class="comment">equations. </span></div> |
| <div class="line"><a name="l00091"></a><span class="lineno"> 91</span> <span class="comment"></DD></span></div> |
| <div class="line"><a name="l00092"></a><span class="lineno"> 92</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00093"></a><span class="lineno"> 93</span> <span class="comment"><DT>tbl_result</DT></span></div> |
| <div class="line"><a name="l00094"></a><span class="lineno"> 94</span> <span class="comment"><DD>Text value. The name of the table where the output is saved.</DD></span></div> |
| <div class="line"><a name="l00095"></a><span class="lineno"> 95</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00096"></a><span class="lineno"> 96</span> <span class="comment"><DT>row_id</DT></span></div> |
| <div class="line"><a name="l00097"></a><span class="lineno"> 97</span> <span class="comment"><DD>Text value. The name of the column storing the 'row id' of the equations.</DD></span></div> |
| <div class="line"><a name="l00098"></a><span class="lineno"> 98</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00099"></a><span class="lineno"> 99</span> <span class="comment">\note For a system with N equations, the row_id's must be a continuous</span></div> |
| <div class="line"><a name="l00100"></a><span class="lineno"> 100</span> <span class="comment">range of integers from \f$ 0 \ldots n-1 \f$.</span></div> |
| <div class="line"><a name="l00101"></a><span class="lineno"> 101</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00102"></a><span class="lineno"> 102</span> <span class="comment"><DT>LHS</DT></span></div> |
| <div class="line"><a name="l00103"></a><span class="lineno"> 103</span> <span class="comment"><DD>Text value. The name of the column storing the 'left hand side' of the </span></div> |
| <div class="line"><a name="l00104"></a><span class="lineno"> 104</span> <span class="comment">equations stored as an array.</DD></span></div> |
| <div class="line"><a name="l00105"></a><span class="lineno"> 105</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00106"></a><span class="lineno"> 106</span> <span class="comment"><DT>RHS</DT></span></div> |
| <div class="line"><a name="l00107"></a><span class="lineno"> 107</span> <span class="comment"><DD>Text value. The name of the column storing the 'right hand side' of the </span></div> |
| <div class="line"><a name="l00108"></a><span class="lineno"> 108</span> <span class="comment">equations.</DD></span></div> |
| <div class="line"><a name="l00109"></a><span class="lineno"> 109</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00110"></a><span class="lineno"> 110</span> <span class="comment"><DT>grouping_col (optional) </DT></span></div> |
| <div class="line"><a name="l00111"></a><span class="lineno"> 111</span> <span class="comment"><DD>Text value. Group by columns. Default: NULL.</DD></span></div> |
| <div class="line"><a name="l00112"></a><span class="lineno"> 112</span> <span class="comment">\note The grouing columns is a placeholder in MADlib V1.1</span></div> |
| <div class="line"><a name="l00113"></a><span class="lineno"> 113</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00114"></a><span class="lineno"> 114</span> <span class="comment"><DT>optimizer (optional) </DT></span></div> |
| <div class="line"><a name="l00115"></a><span class="lineno"> 115</span> <span class="comment"><DD>Text value. Type of optimizer. Default: 'direct'.</DD></span></div> |
| <div class="line"><a name="l00116"></a><span class="lineno"> 116</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00117"></a><span class="lineno"> 117</span> <span class="comment"><DT>optimizer_params (optional) </DT></span></div> |
| <div class="line"><a name="l00118"></a><span class="lineno"> 118</span> <span class="comment"><DD>Text value. Optimizer specific parameters. Default: NULL.</DD></span></div> |
| <div class="line"><a name="l00119"></a><span class="lineno"> 119</span> <span class="comment"></DL></span></div> |
| <div class="line"><a name="l00120"></a><span class="lineno"> 120</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00121"></a><span class="lineno"> 121</span> <span class="comment">@anchor dls_opt_params</span></div> |
| <div class="line"><a name="l00122"></a><span class="lineno"> 122</span> <span class="comment">@par Optimizer Parameters</span></div> |
| <div class="line"><a name="l00123"></a><span class="lineno"> 123</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00124"></a><span class="lineno"> 124</span> <span class="comment">For each optimizer, there are specific parameters that can be tuned</span></div> |
| <div class="line"><a name="l00125"></a><span class="lineno"> 125</span> <span class="comment">for better performance.</span></div> |
| <div class="line"><a name="l00126"></a><span class="lineno"> 126</span> <span class="comment">\par</span></div> |
| <div class="line"><a name="l00127"></a><span class="lineno"> 127</span> <span class="comment"><DL class="arglist"></span></div> |
| <div class="line"><a name="l00128"></a><span class="lineno"> 128</span> <span class="comment"><DT>algorithm (default: householderqr)</dT></span></div> |
| <div class="line"><a name="l00129"></a><span class="lineno"> 129</span> <span class="comment"><DD></span></div> |
| <div class="line"><a name="l00130"></a><span class="lineno"> 130</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00131"></a><span class="lineno"> 131</span> <span class="comment"> There are several algorithms that can be classified as 'direct' methods</span></div> |
| <div class="line"><a name="l00132"></a><span class="lineno"> 132</span> <span class="comment"> of solving linear systems. MADlib dense linear system solvers provide </span></div> |
| <div class="line"><a name="l00133"></a><span class="lineno"> 133</span> <span class="comment"> various algorithmic options for users.</span></div> |
| <div class="line"><a name="l00134"></a><span class="lineno"> 134</span> <span class="comment"> </span></div> |
| <div class="line"><a name="l00135"></a><span class="lineno"> 135</span> <span class="comment"> The following table provides a guideline on the choice of algorithm based </span></div> |
| <div class="line"><a name="l00136"></a><span class="lineno"> 136</span> <span class="comment"> on conditions on the A matrix, speed of the algorithms and numerical stability.</span></div> |
| <div class="line"><a name="l00137"></a><span class="lineno"> 137</span> <span class="comment"> </span></div> |
| <div class="line"><a name="l00138"></a><span class="lineno"> 138</span> <span class="comment"> Algorithm | Contitions on A | Speed | Accuracy</span></div> |
| <div class="line"><a name="l00139"></a><span class="lineno"> 139</span> <span class="comment"> ----------------------------------------------------------</span></div> |
| <div class="line"><a name="l00140"></a><span class="lineno"> 140</span> <span class="comment"> householderqr | None | ++ | +</span></div> |
| <div class="line"><a name="l00141"></a><span class="lineno"> 141</span> <span class="comment"> partialpivlu | Invertable | ++ | +</span></div> |
| <div class="line"><a name="l00142"></a><span class="lineno"> 142</span> <span class="comment"> fullpivlu | None | - | +++ </span></div> |
| <div class="line"><a name="l00143"></a><span class="lineno"> 143</span> <span class="comment"> colpivhouseholderqr | None | + | ++</span></div> |
| <div class="line"><a name="l00144"></a><span class="lineno"> 144</span> <span class="comment"> fullpivhouseholderqr | None | - | +++</span></div> |
| <div class="line"><a name="l00145"></a><span class="lineno"> 145</span> <span class="comment"> llt | Pos. Definite | +++ | +</span></div> |
| <div class="line"><a name="l00146"></a><span class="lineno"> 146</span> <span class="comment"> ldlt | Pos. or Neg Def | +++ | ++</span></div> |
| <div class="line"><a name="l00147"></a><span class="lineno"> 147</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00148"></a><span class="lineno"> 148</span> <span class="comment"> For speed '++' is faster than '+', which is faster than '-'.</span></div> |
| <div class="line"><a name="l00149"></a><span class="lineno"> 149</span> <span class="comment"> For accuracy '+++' is better than '++'.</span></div> |
| <div class="line"><a name="l00150"></a><span class="lineno"> 150</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00151"></a><span class="lineno"> 151</span> <span class="comment"> More details about the individual algorithms can be found on the <a href="http://eigen.tuxfamily.org/dox-devel/group__TutorialLinearAlgebra.html"> Eigen documentation</a>. Eigen is an open source library for linear algebra.</span></div> |
| <div class="line"><a name="l00152"></a><span class="lineno"> 152</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00153"></a><span class="lineno"> 153</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00154"></a><span class="lineno"> 154</span> <span class="comment"></DD></span></div> |
| <div class="line"><a name="l00155"></a><span class="lineno"> 155</span> <span class="comment"></DL></span></div> |
| <div class="line"><a name="l00156"></a><span class="lineno"> 156</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00157"></a><span class="lineno"> 157</span> <span class="comment">@anchor dls_output</span></div> |
| <div class="line"><a name="l00158"></a><span class="lineno"> 158</span> <span class="comment">@par Output statistics </span></div> |
| <div class="line"><a name="l00159"></a><span class="lineno"> 159</span> <span class="comment">Output is stored in the <em>tbl_result</em> table. </span></div> |
| <div class="line"><a name="l00160"></a><span class="lineno"> 160</span> <span class="comment"><DL class="arglist"></span></div> |
| <div class="line"><a name="l00161"></a><span class="lineno"> 161</span> <span class="comment"><DT>solution</dT></span></div> |
| <div class="line"><a name="l00162"></a><span class="lineno"> 162</span> <span class="comment"><DD></span></div> |
| <div class="line"><a name="l00163"></a><span class="lineno"> 163</span> <span class="comment">The solution is an array (of double precision) with the variables in the same</span></div> |
| <div class="line"><a name="l00164"></a><span class="lineno"> 164</span> <span class="comment">order as that provided as input in the 'left_hand_side' column name of the</span></div> |
| <div class="line"><a name="l00165"></a><span class="lineno"> 165</span> <span class="comment">'source_table'</span></div> |
| <div class="line"><a name="l00166"></a><span class="lineno"> 166</span> <span class="comment"></DD></span></div> |
| <div class="line"><a name="l00167"></a><span class="lineno"> 167</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00168"></a><span class="lineno"> 168</span> <span class="comment"><DT>residual_norm</dT></span></div> |
| <div class="line"><a name="l00169"></a><span class="lineno"> 169</span> <span class="comment"><DD></span></div> |
| <div class="line"><a name="l00170"></a><span class="lineno"> 170</span> <span class="comment">Computes the scaled residual norm, defined as \f$ \frac{|Ax - b|}{|b|} \f$. </span></div> |
| <div class="line"><a name="l00171"></a><span class="lineno"> 171</span> <span class="comment">This value is an indication of the accuracy of the solution.</span></div> |
| <div class="line"><a name="l00172"></a><span class="lineno"> 172</span> <span class="comment"></DD></span></div> |
| <div class="line"><a name="l00173"></a><span class="lineno"> 173</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00174"></a><span class="lineno"> 174</span> <span class="comment"><DT>iters</dT></span></div> |
| <div class="line"><a name="l00175"></a><span class="lineno"> 175</span> <span class="comment"><DD>`</span></div> |
| <div class="line"><a name="l00176"></a><span class="lineno"> 176</span> <span class="comment">The number of iterations required by the algorithm (only applicable for </span></div> |
| <div class="line"><a name="l00177"></a><span class="lineno"> 177</span> <span class="comment"> iterative algorithms). The output is NULL for</span></div> |
| <div class="line"><a name="l00178"></a><span class="lineno"> 178</span> <span class="comment">'direct' methods. </span></div> |
| <div class="line"><a name="l00179"></a><span class="lineno"> 179</span> <span class="comment"></DD></span></div> |
| <div class="line"><a name="l00180"></a><span class="lineno"> 180</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00181"></a><span class="lineno"> 181</span> <span class="comment"></DL></span></div> |
| <div class="line"><a name="l00182"></a><span class="lineno"> 182</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00183"></a><span class="lineno"> 183</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00184"></a><span class="lineno"> 184</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00185"></a><span class="lineno"> 185</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00186"></a><span class="lineno"> 186</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00187"></a><span class="lineno"> 187</span> <span class="comment">@anchor dls_examples</span></div> |
| <div class="line"><a name="l00188"></a><span class="lineno"> 188</span> <span class="comment">@examp</span></div> |
| <div class="line"><a name="l00189"></a><span class="lineno"> 189</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00190"></a><span class="lineno"> 190</span> <span class="comment">-# Create the sample data set:</span></div> |
| <div class="line"><a name="l00191"></a><span class="lineno"> 191</span> <span class="comment">\verbatim</span></div> |
| <div class="line"><a name="l00192"></a><span class="lineno"> 192</span> <span class="comment">sql> CREATE TABLE linear_systems_test_data (id INTEGER NOT NULL, </span></div> |
| <div class="line"><a name="l00193"></a><span class="lineno"> 193</span> <span class="comment"> lhs DOUBLE PRECISION[],</span></div> |
| <div class="line"><a name="l00194"></a><span class="lineno"> 194</span> <span class="comment"> rhs DOUBLE PRECISION);</span></div> |
| <div class="line"><a name="l00195"></a><span class="lineno"> 195</span> <span class="comment">sql> INSERT INTO linear_systems_test_data(id, lhs, rhs) VaLUES</span></div> |
| <div class="line"><a name="l00196"></a><span class="lineno"> 196</span> <span class="comment"> (0, ARRAY[1,0,0], 20),</span></div> |
| <div class="line"><a name="l00197"></a><span class="lineno"> 197</span> <span class="comment"> (1, ARRAY[0,1,0], 15),</span></div> |
| <div class="line"><a name="l00198"></a><span class="lineno"> 198</span> <span class="comment"> (2, ARRAY[0,0,1], 20);</span></div> |
| <div class="line"><a name="l00199"></a><span class="lineno"> 199</span> <span class="comment">\endverbatim</span></div> |
| <div class="line"><a name="l00200"></a><span class="lineno"> 200</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00201"></a><span class="lineno"> 201</span> <span class="comment">-# Solve the linear systems with default parameters</span></div> |
| <div class="line"><a name="l00202"></a><span class="lineno"> 202</span> <span class="comment">\verbatim</span></div> |
| <div class="line"><a name="l00203"></a><span class="lineno"> 203</span> <span class="comment">sql> SELECT madlib.linear_solver_dense('linear_systems_test_data', </span></div> |
| <div class="line"><a name="l00204"></a><span class="lineno"> 204</span> <span class="comment"> 'output_table', </span></div> |
| <div class="line"><a name="l00205"></a><span class="lineno"> 205</span> <span class="comment"> 'id',</span></div> |
| <div class="line"><a name="l00206"></a><span class="lineno"> 206</span> <span class="comment"> 'lhs',</span></div> |
| <div class="line"><a name="l00207"></a><span class="lineno"> 207</span> <span class="comment"> 'rhs');</span></div> |
| <div class="line"><a name="l00208"></a><span class="lineno"> 208</span> <span class="comment">\endverbatim</span></div> |
| <div class="line"><a name="l00209"></a><span class="lineno"> 209</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00210"></a><span class="lineno"> 210</span> <span class="comment">-# Obtain the output from the output table</span></div> |
| <div class="line"><a name="l00211"></a><span class="lineno"> 211</span> <span class="comment">\verbatim</span></div> |
| <div class="line"><a name="l00212"></a><span class="lineno"> 212</span> <span class="comment">sql> SELECT * FROM output_table;</span></div> |
| <div class="line"><a name="l00213"></a><span class="lineno"> 213</span> <span class="comment">--------------------+-------------------------------------</span></div> |
| <div class="line"><a name="l00214"></a><span class="lineno"> 214</span> <span class="comment">solution | {20,15,20}</span></div> |
| <div class="line"><a name="l00215"></a><span class="lineno"> 215</span> <span class="comment">residual_norm | 0</span></div> |
| <div class="line"><a name="l00216"></a><span class="lineno"> 216</span> <span class="comment">iters | NULL</span></div> |
| <div class="line"><a name="l00217"></a><span class="lineno"> 217</span> <span class="comment">\endverbatim</span></div> |
| <div class="line"><a name="l00218"></a><span class="lineno"> 218</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00219"></a><span class="lineno"> 219</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00220"></a><span class="lineno"> 220</span> <span class="comment">-# Chose a different algorithm than the default algorithm</span></div> |
| <div class="line"><a name="l00221"></a><span class="lineno"> 221</span> <span class="comment">\verbatim</span></div> |
| <div class="line"><a name="l00222"></a><span class="lineno"> 222</span> <span class="comment">drop table if exists result_table;</span></div> |
| <div class="line"><a name="l00223"></a><span class="lineno"> 223</span> <span class="comment">select madlib.linear_solver_dense(</span></div> |
| <div class="line"><a name="l00224"></a><span class="lineno"> 224</span> <span class="comment"> 'linear_systems_test_data',</span></div> |
| <div class="line"><a name="l00225"></a><span class="lineno"> 225</span> <span class="comment"> 'result_table',</span></div> |
| <div class="line"><a name="l00226"></a><span class="lineno"> 226</span> <span class="comment"> 'id',</span></div> |
| <div class="line"><a name="l00227"></a><span class="lineno"> 227</span> <span class="comment"> 'lhs',</span></div> |
| <div class="line"><a name="l00228"></a><span class="lineno"> 228</span> <span class="comment"> 'rhs',</span></div> |
| <div class="line"><a name="l00229"></a><span class="lineno"> 229</span> <span class="comment"> NULL,</span></div> |
| <div class="line"><a name="l00230"></a><span class="lineno"> 230</span> <span class="comment"> 'direct',</span></div> |
| <div class="line"><a name="l00231"></a><span class="lineno"> 231</span> <span class="comment"> 'algorithm=llt'</span></div> |
| <div class="line"><a name="l00232"></a><span class="lineno"> 232</span> <span class="comment"> );</span></div> |
| <div class="line"><a name="l00233"></a><span class="lineno"> 233</span> <span class="comment">\endverbatim</span></div> |
| <div class="line"><a name="l00234"></a><span class="lineno"> 234</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00235"></a><span class="lineno"> 235</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00236"></a><span class="lineno"> 236</span> <span class="comment">@sa File dense_linear_sytems.sql_in documenting the SQL functions.</span></div> |
| <div class="line"><a name="l00237"></a><span class="lineno"> 237</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00238"></a><span class="lineno"> 238</span> <span class="comment">@internal</span></div> |
| <div class="line"><a name="l00239"></a><span class="lineno"> 239</span> <span class="comment">@sa Namespace \ref madlib::modules::linear_systems documenting the implementation in C++</span></div> |
| <div class="line"><a name="l00240"></a><span class="lineno"> 240</span> <span class="comment">@endinternal</span></div> |
| <div class="line"><a name="l00241"></a><span class="lineno"> 241</span> <span class="comment">*/</span></div> |
| <div class="line"><a name="l00242"></a><span class="lineno"> 242</span> </div> |
| <div class="line"><a name="l00243"></a><span class="lineno"> 243</span> ------------------ Linear Systems ------------------------------</div> |
| <div class="line"><a name="l00244"></a><span class="lineno"> 244</span> </div> |
| <div class="line"><a name="l00245"></a><span class="lineno"> 245</span> CREATE TYPE MADLIB_SCHEMA.dense_linear_solver_result AS (</div> |
| <div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  solution DOUBLE PRECISION[],</div> |
| <div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  residual_norm DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  iters INTEGER</div> |
| <div class="line"><a name="l00249"></a><span class="lineno"> 249</span> );</div> |
| <div class="line"><a name="l00250"></a><span class="lineno"> 250</span> </div> |
| <div class="line"><a name="l00251"></a><span class="lineno"> 251</span> CREATE TYPE MADLIB_SCHEMA.residual_norm_result AS (</div> |
| <div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  residual_norm DOUBLE PRECISION</div> |
| <div class="line"><a name="l00253"></a><span class="lineno"> 253</span> );</div> |
| <div class="line"><a name="l00254"></a><span class="lineno"> 254</span> </div> |
| <div class="line"><a name="l00255"></a><span class="lineno"> 255</span> </div> |
| <div class="line"><a name="l00256"></a><span class="lineno"> 256</span> ------------------------ Compute the residuals ------------------------------</div> |
| <div class="line"><a name="l00257"></a><span class="lineno"> 257</span> </div> |
| <div class="line"><a name="l00258"></a><span class="lineno"> 258</span> CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.dense_residual_norm_transition(</div> |
| <div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  state MADLIB_SCHEMA.bytea8,</div> |
| <div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  a DOUBLE PRECISION[],</div> |
| <div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  b DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  x DOUBLE PRECISION[])</div> |
| <div class="line"><a name="l00263"></a><span class="lineno"> 263</span> RETURNS MADLIB_SCHEMA.bytea8</div> |
| <div class="line"><a name="l00264"></a><span class="lineno"> 264</span> AS 'MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00265"></a><span class="lineno"> 265</span> <span class="stringliteral">LANGUAGE C IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00266"></a><span class="lineno"> 266</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00267"></a><span class="lineno"> 267</span> <span class="stringliteral">CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.dense_residual_norm_merge_states(</span></div> |
| <div class="line"><a name="l00268"></a><span class="lineno"> 268</span> <span class="stringliteral"> state1 MADLIB_SCHEMA.bytea8,</span></div> |
| <div class="line"><a name="l00269"></a><span class="lineno"> 269</span> <span class="stringliteral"> state2 MADLIB_SCHEMA.bytea8)</span></div> |
| <div class="line"><a name="l00270"></a><span class="lineno"> 270</span> <span class="stringliteral">RETURNS MADLIB_SCHEMA.bytea8</span></div> |
| <div class="line"><a name="l00271"></a><span class="lineno"> 271</span> <span class="stringliteral">AS '</span>MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00272"></a><span class="lineno"> 272</span> <span class="stringliteral">LANGUAGE C IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00273"></a><span class="lineno"> 273</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00274"></a><span class="lineno"> 274</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00275"></a><span class="lineno"> 275</span> <span class="stringliteral">CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.dense_residual_norm_final(</span></div> |
| <div class="line"><a name="l00276"></a><span class="lineno"> 276</span> <span class="stringliteral"> state MADLIB_SCHEMA.bytea8)</span></div> |
| <div class="line"><a name="l00277"></a><span class="lineno"> 277</span> <span class="stringliteral">RETURNS MADLIB_SCHEMA.residual_norm_result</span></div> |
| <div class="line"><a name="l00278"></a><span class="lineno"> 278</span> <span class="stringliteral">AS '</span>MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00279"></a><span class="lineno"> 279</span> <span class="stringliteral">LANGUAGE C IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00280"></a><span class="lineno"> 280</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00281"></a><span class="lineno"> 281</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00282"></a><span class="lineno"> 282</span> <span class="comment"> * @brief Compute the residual after solving the dense linear systems</span></div> |
| <div class="line"><a name="l00283"></a><span class="lineno"> 283</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00284"></a><span class="lineno"> 284</span> <span class="comment"> * @param left_hand_side Column containing the left hand side of the system</span></div> |
| <div class="line"><a name="l00285"></a><span class="lineno"> 285</span> <span class="comment"> * @param right_hand_side Column containing the right hand side of the system</span></div> |
| <div class="line"><a name="l00286"></a><span class="lineno"> 286</span> <span class="comment"> * @param solution Solution of the linear system</span></div> |
| <div class="line"><a name="l00287"></a><span class="lineno"> 287</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00288"></a><span class="lineno"> 288</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00289"></a><span class="lineno"> 289</span> <span class="comment"> * @return residual_norm FLOAT8:</span></div> |
| <div class="line"><a name="l00290"></a><span class="lineno"> 290</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00291"></a><span class="lineno"> 291</span> <span class="comment"> * @usage</span></div> |
| <div class="line"><a name="l00292"></a><span class="lineno"> 292</span> <span class="comment"> * - Get all the diagnostic statistics:\n</span></div> |
| <div class="line"><a name="l00293"></a><span class="lineno"> 293</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00294"></a><span class="lineno"> 294</span> <span class="comment"> * <pre> SELECT dense_residual_norm(<em>row_id</em>,</span></div> |
| <div class="line"><a name="l00295"></a><span class="lineno"> 295</span> <span class="comment"> * <em>left_hand_side</em>, </span></div> |
| <div class="line"><a name="l00296"></a><span class="lineno"> 296</span> <span class="comment"> * <em> right_hand_side </em>, </span></div> |
| <div class="line"><a name="l00297"></a><span class="lineno"> 297</span> <span class="comment"> * <em> solution </em>)</span></div> |
| <div class="line"><a name="l00298"></a><span class="lineno"> 298</span> <span class="comment"> * FROM <em>dataTable</em>;</span></div> |
| <div class="line"><a name="l00299"></a><span class="lineno"> 299</span> <span class="comment"> * </pre></span></div> |
| <div class="line"><a name="l00300"></a><span class="lineno"> 300</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00301"></a><span class="lineno"> 301</span> </div> |
| <div class="line"><a name="l00302"></a><span class="lineno"> 302</span> CREATE AGGREGATE MADLIB_SCHEMA.dense_residual_norm(</div> |
| <div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  /*+ "left_hand_side" */ DOUBLE PRECISION[],</div> |
| <div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  /*+ "right_hand_side" */ DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  /*+ "solution" */ DOUBLE PRECISION[])(</div> |
| <div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  STYPE=MADLIB_SCHEMA.bytea8,</div> |
| <div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  SFUNC=MADLIB_SCHEMA.dense_residual_norm_transition,</div> |
| <div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  m4_ifdef(`__GREENPLUM__',`PREFUNC=MADLIB_SCHEMA.dense_residual_norm_merge_states,<span class="stringliteral">')</span></div> |
| <div class="line"><a name="l00309"></a><span class="lineno"> 309</span> <span class="stringliteral"> FINALFUNC=MADLIB_SCHEMA.dense_residual_norm_final,</span></div> |
| <div class="line"><a name="l00310"></a><span class="lineno"> 310</span> <span class="stringliteral"> INITCOND='</span><span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00311"></a><span class="lineno"> 311</span> <span class="stringliteral">);</span></div> |
| <div class="line"><a name="l00312"></a><span class="lineno"> 312</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00313"></a><span class="lineno"> 313</span> <span class="stringliteral">------------------ Direct Method ------------------------------</span></div> |
| <div class="line"><a name="l00314"></a><span class="lineno"> 314</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00315"></a><span class="lineno"> 315</span> <span class="stringliteral">CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.dense_direct_linear_system_transition(</span></div> |
| <div class="line"><a name="l00316"></a><span class="lineno"> 316</span> <span class="stringliteral"> state DOUBLE PRECISION[],</span></div> |
| <div class="line"><a name="l00317"></a><span class="lineno"> 317</span> <span class="stringliteral"> row_id INTEGER,</span></div> |
| <div class="line"><a name="l00318"></a><span class="lineno"> 318</span> <span class="stringliteral"> a DOUBLE PRECISION[],</span></div> |
| <div class="line"><a name="l00319"></a><span class="lineno"> 319</span> <span class="stringliteral"> b DOUBLE PRECISION,</span></div> |
| <div class="line"><a name="l00320"></a><span class="lineno"> 320</span> <span class="stringliteral"> num_rows INTEGER,</span></div> |
| <div class="line"><a name="l00321"></a><span class="lineno"> 321</span> <span class="stringliteral"> algorithm INTEGER)</span></div> |
| <div class="line"><a name="l00322"></a><span class="lineno"> 322</span> <span class="stringliteral">RETURNS DOUBLE PRECISION[]</span></div> |
| <div class="line"><a name="l00323"></a><span class="lineno"> 323</span> <span class="stringliteral">AS '</span>MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00324"></a><span class="lineno"> 324</span> <span class="stringliteral">LANGUAGE C IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00325"></a><span class="lineno"> 325</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00326"></a><span class="lineno"> 326</span> <span class="stringliteral">CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.dense_direct_linear_system_merge_states(</span></div> |
| <div class="line"><a name="l00327"></a><span class="lineno"> 327</span> <span class="stringliteral"> state1 DOUBLE PRECISION[],</span></div> |
| <div class="line"><a name="l00328"></a><span class="lineno"> 328</span> <span class="stringliteral"> state2 DOUBLE PRECISION[])</span></div> |
| <div class="line"><a name="l00329"></a><span class="lineno"> 329</span> <span class="stringliteral">RETURNS DOUBLE PRECISION[]</span></div> |
| <div class="line"><a name="l00330"></a><span class="lineno"> 330</span> <span class="stringliteral">AS '</span>MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00331"></a><span class="lineno"> 331</span> <span class="stringliteral">LANGUAGE C IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00332"></a><span class="lineno"> 332</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00333"></a><span class="lineno"> 333</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00334"></a><span class="lineno"> 334</span> <span class="stringliteral">CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.dense_direct_linear_system_final(</span></div> |
| <div class="line"><a name="l00335"></a><span class="lineno"> 335</span> <span class="stringliteral"> state DOUBLE PRECISION[])</span></div> |
| <div class="line"><a name="l00336"></a><span class="lineno"> 336</span> <span class="stringliteral">RETURNS MADLIB_SCHEMA.dense_linear_solver_result</span></div> |
| <div class="line"><a name="l00337"></a><span class="lineno"> 337</span> <span class="stringliteral">AS '</span>MODULE_PATHNAME<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00338"></a><span class="lineno"> 338</span> <span class="stringliteral">LANGUAGE C IMMUTABLE STRICT;</span></div> |
| <div class="line"><a name="l00339"></a><span class="lineno"> 339</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00340"></a><span class="lineno"> 340</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00341"></a><span class="lineno"> 341</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00342"></a><span class="lineno"> 342</span> <span class="comment"> * @brief Solve a system of linear equations using the direct method</span></div> |
| <div class="line"><a name="l00343"></a><span class="lineno"> 343</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00344"></a><span class="lineno"> 344</span> <span class="comment"> * @param row_id Column containing the row_id</span></div> |
| <div class="line"><a name="l00345"></a><span class="lineno"> 345</span> <span class="comment"> * @param left_hand_side Column containing the left hand side of the system</span></div> |
| <div class="line"><a name="l00346"></a><span class="lineno"> 346</span> <span class="comment"> * @param right_hand_side Column containing the right hand side of the system</span></div> |
| <div class="line"><a name="l00347"></a><span class="lineno"> 347</span> <span class="comment"> * @param numEquations Number of equations</span></div> |
| <div class="line"><a name="l00348"></a><span class="lineno"> 348</span> <span class="comment"> * @param algorithm Algorithm used for the dense linear solver</span></div> |
| <div class="line"><a name="l00349"></a><span class="lineno"> 349</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00350"></a><span class="lineno"> 350</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00351"></a><span class="lineno"> 351</span> <span class="comment"> * @return A composite value:</span></div> |
| <div class="line"><a name="l00352"></a><span class="lineno"> 352</span> <span class="comment"> * - <tt>solution FLOAT8[] </tt> - Array of marginal effects</span></div> |
| <div class="line"><a name="l00353"></a><span class="lineno"> 353</span> <span class="comment"> * - <tt>residual_norm FLOAT8</tt> - Norm of the residual </span></div> |
| <div class="line"><a name="l00354"></a><span class="lineno"> 354</span> <span class="comment"> * - <tt>iters INTEGER</tt> - Iterations taken</span></div> |
| <div class="line"><a name="l00355"></a><span class="lineno"> 355</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00356"></a><span class="lineno"> 356</span> <span class="comment"> * @usage</span></div> |
| <div class="line"><a name="l00357"></a><span class="lineno"> 357</span> <span class="comment"> * - Get all the diagnostic statistics:\n</span></div> |
| <div class="line"><a name="l00358"></a><span class="lineno"> 358</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00359"></a><span class="lineno"> 359</span> <span class="comment"> * <pre> SELECT linear_system_dense(<em>row_id</em>,</span></div> |
| <div class="line"><a name="l00360"></a><span class="lineno"> 360</span> <span class="comment"> * <em>left_hand_side</em>, </span></div> |
| <div class="line"><a name="l00361"></a><span class="lineno"> 361</span> <span class="comment"> * <em> right_hand_side </em>, </span></div> |
| <div class="line"><a name="l00362"></a><span class="lineno"> 362</span> <span class="comment"> * <em> numEquations </em>)</span></div> |
| <div class="line"><a name="l00363"></a><span class="lineno"> 363</span> <span class="comment"> * FROM <em>dataTable</em>;</span></div> |
| <div class="line"><a name="l00364"></a><span class="lineno"> 364</span> <span class="comment"> * </pre></span></div> |
| <div class="line"><a name="l00365"></a><span class="lineno"> 365</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00366"></a><span class="lineno"> 366</span> </div> |
| <div class="line"><a name="l00367"></a><span class="lineno"> 367</span> CREATE AGGREGATE MADLIB_SCHEMA.dense_direct_linear_system(</div> |
| <div class="line"><a name="l00368"></a><span class="lineno"> 368</span>  /*+ "row_id" */ INTEGER,</div> |
| <div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  /*+ "left_hand_side" */ DOUBLE PRECISION[],</div> |
| <div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  /*+ "right_hand_side" */ DOUBLE PRECISION,</div> |
| <div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  /*+ "numEquations" */ INTEGER,</div> |
| <div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  /*+ "algorithm" */ INTEGER)(</div> |
| <div class="line"><a name="l00373"></a><span class="lineno"> 373</span>  STYPE=DOUBLE PRECISION[],</div> |
| <div class="line"><a name="l00374"></a><span class="lineno"> 374</span>  SFUNC=MADLIB_SCHEMA.dense_direct_linear_system_transition,</div> |
| <div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  m4_ifdef(`__GREENPLUM__',`PREFUNC=MADLIB_SCHEMA.dense_direct_linear_system_merge_states,<span class="stringliteral">')</span></div> |
| <div class="line"><a name="l00376"></a><span class="lineno"> 376</span> <span class="stringliteral"> FINALFUNC=MADLIB_SCHEMA.dense_direct_linear_system_final,</span></div> |
| <div class="line"><a name="l00377"></a><span class="lineno"> 377</span> <span class="stringliteral"> INITCOND='</span>{0,0,0,0,0,0}<span class="stringliteral">'</span></div> |
| <div class="line"><a name="l00378"></a><span class="lineno"> 378</span> <span class="stringliteral">);</span></div> |
| <div class="line"><a name="l00379"></a><span class="lineno"> 379</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00380"></a><span class="lineno"> 380</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00381"></a><span class="lineno"> 381</span> <span class="stringliteral">--------------------------- Interface ----------------------------------</span></div> |
| <div class="line"><a name="l00382"></a><span class="lineno"> 382</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00383"></a><span class="lineno"> 383</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00384"></a><span class="lineno"> 384</span> <span class="comment"> * @brief Help function, to print out the supported families</span></div> |
| <div class="line"><a name="l00385"></a><span class="lineno"> 385</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00386"></a><span class="lineno"> 386</span> CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.linear_solver_dense(</div> |
| <div class="line"><a name="l00387"></a><span class="lineno"> 387</span>  input_string VARCHAR</div> |
| <div class="line"><a name="l00388"></a><span class="lineno"> 388</span> )</div> |
| <div class="line"><a name="l00389"></a><span class="lineno"> 389</span> RETURNS VARCHAR AS $$</div> |
| <div class="line"><a name="l00390"></a><span class="lineno"> 390</span> PythonFunction(linear_systems, dense_linear_systems, linear_solver_dense_help)</div> |
| <div class="line"><a name="l00391"></a><span class="lineno"> 391</span> $$ LANGUAGE plpythonu;</div> |
| <div class="line"><a name="l00392"></a><span class="lineno"> 392</span> </div> |
| <div class="line"><a name="l00393"></a><span class="lineno"> 393</span> CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.linear_solver_dense()</div> |
| <div class="line"><a name="l00394"></a><span class="lineno"> 394</span> RETURNS VARCHAR AS $$</div> |
| <div class="line"><a name="l00395"></a><span class="lineno"> 395</span> BEGIN</div> |
| <div class="line"><a name="l00396"></a><span class="lineno"> 396</span>  RETURN MADLIB_SCHEMA.linear_solver_dense('<span class="stringliteral">');</span></div> |
| <div class="line"><a name="l00397"></a><span class="lineno"> 397</span> <span class="stringliteral">END;</span></div> |
| <div class="line"><a name="l00398"></a><span class="lineno"> 398</span> <span class="stringliteral">$$ LANGUAGE plpgsql VOLATILE;</span></div> |
| <div class="line"><a name="l00399"></a><span class="lineno"> 399</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00400"></a><span class="lineno"> 400</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00401"></a><span class="lineno"> 401</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00402"></a><span class="lineno"> 402</span> <span class="comment"> @brief A wrapper function for the various marginal linear_systemsion analyzes.</span></div> |
| <div class="line"><a name="l00403"></a><span class="lineno"> 403</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00404"></a><span class="lineno"> 404</span> <span class="comment"> * @param source_table String identifying the input table</span></div> |
| <div class="line"><a name="l00405"></a><span class="lineno"> 405</span> <span class="comment"> * @param out_table String identifying the output table to be created</span></div> |
| <div class="line"><a name="l00406"></a><span class="lineno"> 406</span> <span class="comment"> * @param row_id Column containing the row_id</span></div> |
| <div class="line"><a name="l00407"></a><span class="lineno"> 407</span> <span class="comment"> * @param left_hand_side Column containing the left hand side of the system</span></div> |
| <div class="line"><a name="l00408"></a><span class="lineno"> 408</span> <span class="comment"> * @param right_hand_side Column containing the right hand side of the system</span></div> |
| <div class="line"><a name="l00409"></a><span class="lineno"> 409</span> <span class="comment"> * @param grouping_cols Columns to group by</span></div> |
| <div class="line"><a name="l00410"></a><span class="lineno"> 410</span> <span class="comment"> * @param optimzer Optimizer to be used </span></div> |
| <div class="line"><a name="l00411"></a><span class="lineno"> 411</span> <span class="comment"> * @param optimzer_options Optimal parameters for the algorithms</span></div> |
| <div class="line"><a name="l00412"></a><span class="lineno"> 412</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00413"></a><span class="lineno"> 413</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00414"></a><span class="lineno"> 414</span> <span class="comment"> * @return void</span></div> |
| <div class="line"><a name="l00415"></a><span class="lineno"> 415</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00416"></a><span class="lineno"> 416</span> <span class="comment"> * @usage</span></div> |
| <div class="line"><a name="l00417"></a><span class="lineno"> 417</span> <span class="comment"> * For function summary information. Run</span></div> |
| <div class="line"><a name="l00418"></a><span class="lineno"> 418</span> <span class="comment"> * sql> select linear_solver_dense('help');</span></div> |
| <div class="line"><a name="l00419"></a><span class="lineno"> 419</span> <span class="comment"> * OR</span></div> |
| <div class="line"><a name="l00420"></a><span class="lineno"> 420</span> <span class="comment"> * sql> select linear_solver_dense();</span></div> |
| <div class="line"><a name="l00421"></a><span class="lineno"> 421</span> <span class="comment"> * OR</span></div> |
| <div class="line"><a name="l00422"></a><span class="lineno"> 422</span> <span class="comment"> * sql> select linear_solver_dense('?');</span></div> |
| <div class="line"><a name="l00423"></a><span class="lineno"> 423</span> <span class="comment"> * For function usage information. Run</span></div> |
| <div class="line"><a name="l00424"></a><span class="lineno"> 424</span> <span class="comment"> * sql> select linear_solver_dense('usage');</span></div> |
| <div class="line"><a name="l00425"></a><span class="lineno"> 425</span> <span class="comment"> *</span></div> |
| <div class="line"><a name="l00426"></a><span class="lineno"> 426</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00427"></a><span class="lineno"> 427</span> </div> |
| <div class="line"><a name="l00428"></a><span class="lineno"> 428</span> CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.linear_solver_dense(</div> |
| <div class="line"><a name="l00429"></a><span class="lineno"> 429</span>  source_table VARCHAR -- name of input table</div> |
| <div class="line"><a name="l00430"></a><span class="lineno"> 430</span>  , out_table VARCHAR -- name of output table</div> |
| <div class="line"><a name="l00431"></a><span class="lineno"> 431</span>  , row_id VARCHAR -- name of the column containing row_id</div> |
| <div class="line"><a name="l00432"></a><span class="lineno"> 432</span>  , left_hand_side VARCHAR -- name of columns with lhs</div> |
| <div class="line"><a name="l00433"></a><span class="lineno"> 433</span>  , right_hand_side VARCHAR -- name of columns with rhs</div> |
| <div class="line"><a name="l00434"></a><span class="lineno"> 434</span>  , grouping_cols VARCHAR -- name of columns to group by</div> |
| <div class="line"><a name="l00435"></a><span class="lineno"> 435</span>  , optimizer VARCHAR -- Name of the optimizer</div> |
| <div class="line"><a name="l00436"></a><span class="lineno"> 436</span>  , optimizer_options VARCHAR -- Optimal parameters of the optimizer</div> |
| <div class="line"><a name="l00437"></a><span class="lineno"> 437</span>  )</div> |
| <div class="line"><a name="l00438"></a><span class="lineno"> 438</span> RETURNS VOID AS $$</div> |
| <div class="line"><a name="l00439"></a><span class="lineno"> 439</span> PythonFunction(linear_systems, dense_linear_systems, linear_solver_dense)</div> |
| <div class="line"><a name="l00440"></a><span class="lineno"> 440</span> $$ LANGUAGE plpythonu;</div> |
| <div class="line"><a name="l00441"></a><span class="lineno"> 441</span> </div> |
| <div class="line"><a name="l00442"></a><span class="lineno"> 442</span> </div> |
| <div class="line"><a name="l00443"></a><span class="lineno"> 443</span> </div> |
| <div class="line"><a name="l00444"></a><span class="lineno"> 444</span> -- Default Variable calls for linear_solver_dense</div> |
| <div class="line"><a name="l00445"></a><span class="lineno"> 445</span> ------------------------------------------------------------------------------</div> |
| <div class="line"><a name="l00446"></a><span class="lineno"> 446</span> <span class="comment"></span></div> |
| <div class="line"><a name="l00447"></a><span class="lineno"> 447</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00448"></a><span class="lineno"> 448</span> <span class="comment"> * @brief Marginal effects with default variables</span></div> |
| <div class="line"><a name="l00449"></a><span class="lineno"> 449</span> <span class="comment"> **/</span></div> |
| <div class="line"><a name="l00450"></a><span class="lineno"> 450</span> CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.linear_solver_dense(</div> |
| <div class="line"><a name="l00451"></a><span class="lineno"> 451</span>  source_table VARCHAR -- name of input table</div> |
| <div class="line"><a name="l00452"></a><span class="lineno"> 452</span>  , out_table VARCHAR -- name of output table</div> |
| <div class="line"><a name="l00453"></a><span class="lineno"> 453</span>  , row_id VARCHAR -- name of the column containing row_id</div> |
| <div class="line"><a name="l00454"></a><span class="lineno"> 454</span>  , left_hand_side VARCHAR -- name of columns with lhs</div> |
| <div class="line"><a name="l00455"></a><span class="lineno"> 455</span>  , right_hand_side VARCHAR -- name of columns with rhs</div> |
| <div class="line"><a name="l00456"></a><span class="lineno"> 456</span>  )</div> |
| <div class="line"><a name="l00457"></a><span class="lineno"> 457</span> RETURNS VOID AS $$</div> |
| <div class="line"><a name="l00458"></a><span class="lineno"> 458</span> BEGIN</div> |
| <div class="line"><a name="l00459"></a><span class="lineno"> 459</span>  PERFORM MADLIB_SCHEMA.linear_solver_dense(</div> |
| <div class="line"><a name="l00460"></a><span class="lineno"> 460</span>  source_table,</div> |
| <div class="line"><a name="l00461"></a><span class="lineno"> 461</span>  out_table,</div> |
| <div class="line"><a name="l00462"></a><span class="lineno"> 462</span>  row_id,</div> |
| <div class="line"><a name="l00463"></a><span class="lineno"> 463</span>  left_hand_side,</div> |
| <div class="line"><a name="l00464"></a><span class="lineno"> 464</span>  right_hand_side,</div> |
| <div class="line"><a name="l00465"></a><span class="lineno"> 465</span>  NULL,</div> |
| <div class="line"><a name="l00466"></a><span class="lineno"> 466</span>  'direct<span class="stringliteral">',</span></div> |
| <div class="line"><a name="l00467"></a><span class="lineno"> 467</span> <span class="stringliteral"> NULL);</span></div> |
| <div class="line"><a name="l00468"></a><span class="lineno"> 468</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00469"></a><span class="lineno"> 469</span> <span class="stringliteral">END;</span></div> |
| <div class="line"><a name="l00470"></a><span class="lineno"> 470</span> <span class="stringliteral">$$ LANGUAGE plpgsql VOLATILE;</span></div> |
| <div class="line"><a name="l00471"></a><span class="lineno"> 471</span> <span class="stringliteral"></span></div> |
| <div class="line"><a name="l00472"></a><span class="lineno"> 472</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00473"></a><span class="lineno"> 473</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00474"></a><span class="lineno"> 474</span> <span class="comment"> * @brief Marginal effects with default variables</span></div> |
| <div class="line"><a name="l00475"></a><span class="lineno"> 475</span> <span class="comment"> **/</span></div> |
| <div class="line"><a name="l00476"></a><span class="lineno"> 476</span> CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.linear_solver_dense(</div> |
| <div class="line"><a name="l00477"></a><span class="lineno"> 477</span>  source_table VARCHAR -- name of input table</div> |
| <div class="line"><a name="l00478"></a><span class="lineno"> 478</span>  , out_table VARCHAR -- name of output table</div> |
| <div class="line"><a name="l00479"></a><span class="lineno"> 479</span>  , row_id VARCHAR -- name of the column containing row_id</div> |
| <div class="line"><a name="l00480"></a><span class="lineno"> 480</span>  , left_hand_side VARCHAR -- name of columns with lhs</div> |
| <div class="line"><a name="l00481"></a><span class="lineno"> 481</span>  , right_hand_side VARCHAR -- name of columns with rhs</div> |
| <div class="line"><a name="l00482"></a><span class="lineno"> 482</span>  , grouping_cols VARCHAR -- name of columns to group by</div> |
| <div class="line"><a name="l00483"></a><span class="lineno"> 483</span>  )</div> |
| <div class="line"><a name="l00484"></a><span class="lineno"> 484</span> RETURNS VOID AS $$</div> |
| <div class="line"><a name="l00485"></a><span class="lineno"> 485</span> BEGIN</div> |
| <div class="line"><a name="l00486"></a><span class="lineno"> 486</span>  PERFORM MADLIB_SCHEMA.linear_solver_dense(</div> |
| <div class="line"><a name="l00487"></a><span class="lineno"> 487</span>  source_table,</div> |
| <div class="line"><a name="l00488"></a><span class="lineno"> 488</span>  out_table,</div> |
| <div class="line"><a name="l00489"></a><span class="lineno"> 489</span>  row_id,</div> |
| <div class="line"><a name="l00490"></a><span class="lineno"> 490</span>  left_hand_side,</div> |
| <div class="line"><a name="l00491"></a><span class="lineno"> 491</span>  right_hand_side,</div> |
| <div class="line"><a name="l00492"></a><span class="lineno"> 492</span>  grouping_cols,</div> |
| <div class="line"><a name="l00493"></a><span class="lineno"> 493</span>  'direct<span class="stringliteral">',</span></div> |
| <div class="line"><a name="l00494"></a><span class="lineno"> 494</span> <span class="stringliteral"> NULL);</span></div> |
| <div class="line"><a name="l00495"></a><span class="lineno"> 495</span> <span class="stringliteral">END;</span></div> |
| <div class="line"><a name="l00496"></a><span class="lineno"> 496</span> <span class="stringliteral">$$ LANGUAGE plpgsql VOLATILE;</span></div> |
| <div class="line"><a name="l00497"></a><span class="lineno"> 497</span> <span class="stringliteral"></span><span class="comment"></span></div> |
| <div class="line"><a name="l00498"></a><span class="lineno"> 498</span> <span class="comment">/**</span></div> |
| <div class="line"><a name="l00499"></a><span class="lineno"> 499</span> <span class="comment"> * @brief Marginal effects with default variables</span></div> |
| <div class="line"><a name="l00500"></a><span class="lineno"> 500</span> <span class="comment"> **/</span></div> |
| <div class="line"><a name="l00501"></a><span class="lineno"> 501</span> CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.linear_solver_dense(</div> |
| <div class="line"><a name="l00502"></a><span class="lineno"> 502</span>  source_table VARCHAR -- name of input table</div> |
| <div class="line"><a name="l00503"></a><span class="lineno"> 503</span>  , out_table VARCHAR -- name of output table</div> |
| <div class="line"><a name="l00504"></a><span class="lineno"> 504</span>  , row_id VARCHAR -- name of the column containing row_id</div> |
| <div class="line"><a name="l00505"></a><span class="lineno"> 505</span>  , left_hand_side VARCHAR -- name of columns with lhs</div> |
| <div class="line"><a name="l00506"></a><span class="lineno"> 506</span>  , right_hand_side VARCHAR -- name of columns with rhs</div> |
| <div class="line"><a name="l00507"></a><span class="lineno"> 507</span>  , grouping_cols VARCHAR -- name of columns to group by</div> |
| <div class="line"><a name="l00508"></a><span class="lineno"> 508</span>  , optimizer VARCHAR -- Name of the optimizer</div> |
| <div class="line"><a name="l00509"></a><span class="lineno"> 509</span>  )</div> |
| <div class="line"><a name="l00510"></a><span class="lineno"> 510</span> RETURNS VOID AS $$</div> |
| <div class="line"><a name="l00511"></a><span class="lineno"> 511</span> BEGIN</div> |
| <div class="line"><a name="l00512"></a><span class="lineno"> 512</span>  PERFORM MADLIB_SCHEMA.linear_solver_dense(</div> |
| <div class="line"><a name="l00513"></a><span class="lineno"> 513</span>  source_table,</div> |
| <div class="line"><a name="l00514"></a><span class="lineno"> 514</span>  out_table,</div> |
| <div class="line"><a name="l00515"></a><span class="lineno"> 515</span>  row_id,</div> |
| <div class="line"><a name="l00516"></a><span class="lineno"> 516</span>  left_hand_side,</div> |
| <div class="line"><a name="l00517"></a><span class="lineno"> 517</span>  right_hand_side,</div> |
| <div class="line"><a name="l00518"></a><span class="lineno"> 518</span>  grouping_cols,</div> |
| <div class="line"><a name="l00519"></a><span class="lineno"> 519</span>  optimizer,</div> |
| <div class="line"><a name="l00520"></a><span class="lineno"> 520</span>  NULL);</div> |
| <div class="line"><a name="l00521"></a><span class="lineno"> 521</span> END;</div> |
| <div class="line"><a name="l00522"></a><span class="lineno"> 522</span> $$ LANGUAGE plpgsql VOLATILE;</div> |
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